• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.911-925
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• 2016

We obtain q-derivatives of Srivastava's general triple q-hypergeometric series with respect to its parameters. The particular cases leading to results for three Srivastava's triple q-hypergeometric series $H_{A,q}$, $H_{B,q}$ and $H_{C,q}$ are also considered.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.9 no.6
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• pp.1787-1794
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• 2008

Coenzyme $Q_{10}$ and six derivatives of coenzyme $Q_n$ were synthesized and tested for their antioxidative effects occurred in proximal tubular epithelial cell (LLC-PK1 cell) and cytotoxicities using in NIH/3T3 cell. As the result, synthetic coenzyme $Q_n$ derivatives showed a potent antioxidative effect compared to coenzyme $Q_{10}$. Among these synthetic compounds, coenzyme $Q_3$-C at ranged 0.04 to 0.4 mmol showed the $107.7{\sim}135.9%$ of cell viability in LLC-PK1 cell. In the test of NIH/3T3, all synthesized coenzyme $Q_n$ derivatives showed the similar effect compared with coenzyme $Q_{10}$. A correlation between isoprene unit number of coenzyme $Q_n$ derivatives and its biological effects, we suggest reduction of isoprene unit number of $Q_n$ derivatives may be related to the increase of antioxidants effects and the reduction of cytotoxicities.

• Journal of the Korean Mathematical Society
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• v.55 no.1
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• pp.101-129
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• 2018

From an analytical perspective, we introduce a sequence of Cartier operators that act on the field of formal Laurent series in one variable with coefficients in a field of positive characteristic p. In this work, we discover the binomial inversion formula between Hasse derivatives and Cartier operators, implying that Cartier operators can play a prominent role in various objects of study in function field arithmetic, as a suitable substitute for higher derivatives. For an applicable object, the Wronskian criteria associated with Cartier operators are introduced. These results stem from a careful study of two types of Cartier operators on the power series ring ${\mathbf{F}}_q$[[T]] in one variable T over a finite field ${\mathbf{F}}_q$ of q elements. Accordingly, we show that two sequences of Cartier operators are an orthonormal basis of the space of continuous ${\mathbf{F}}_q$-linear functions on ${\mathbf{F}}_q$[[T]]. According to the digit principle, every continuous function on ${\mathbf{F}}_q$[[T]] is uniquely written in terms of a q-adic extension of Cartier operators, with a closed-form of expansion coefficients for each of the two cases. Moreover, the p-adic analogues of Cartier operators are discussed as orthonormal bases for the space of continuous functions on ${\mathbf{Z}}_p$.

• Journal of Microbiology and Biotechnology
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• v.26 no.9
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• pp.1620-1628
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• 2016

In this study, we investigated colistin resistance mechanisms associated with the regulation of the pbgP operon in Klebsiella pneumoniae, using four isogenic pairs of colistin-susceptible strains and their colistin-resistant derivatives and two colistin-resistant clinical isolates. Amino acid sequence alterations of PhoPQ, PmrAB, and MgrB were investigated, and mRNA expression levels of phoQ, pmrB, pmrD, and pbgP were measured using quantitative real-time PCR. The phoQ and pmrB genes were deleted from two colistin-resistant derivatives, 134R and 063R. We found that phoQ, pmrD, and pbgP were significantly upregulated in all colistin-resistant derivatives. However, pmrB was significantly upregulated in only two colistin-resistant derivatives and one clinical strain. pmrB was not overexpressed in the other strains. The minimum inhibitory concentration of colistin was drastically lower in both phoQ- and pmrB-deleted mutants from a colistin-resistant derivative (134R) that was overexpressing phoQ and pmrB. However, colistin susceptibility was restored only in a phoQ-deleted mutant from a colistin-resistant derivative (063R) without overexpression of pmrB. In conclusion, two different regulations of the pbgP operon may associate with the development of colistinresisant K. pneumoniae.

• Applied Biological Chemistry
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• v.51 no.3
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• pp.164-170
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• 2008

Coenzyme $Q_{10}$ and six derivatives of coenzyme Qn were synthesized and tested for their inhibitory effects on melanogenesis occurred in murine melanoma (B16/F1) cells and on collagenase/elastase activities as well. As the result, synthetic coenzyme Qn showed a potent inhibitory effect on melanin formation, collagenase and elastase activities in all tested concentrations. Among these synthetic compounds, coenzyme $Q_1$ and coenzyme $Q_2$ potentially inhibited melanin formation and elastase activity when compared to other coenzyme Qn derivatives. For the collagenase activities, all coenzyme Qn derivatives inhibited 80-85% of controls. As compared, coenzyme Qn derivatives exhibited strong inhibitory activities with the decrease of isoprenoid unit number of coenzyme Qn derivatives except for collagenase activity. For the inhibition of collagenase activity, moiety of benzoquinone might be considered as the active functional group. Taken together, coenzyme $Q_1$ and coenzyme $Q_2$ might be used for functional cosmetics.

• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.431-452
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• 2022

For any positive integer 𝜇, we compute the mean value of the 𝜇-th derivative of quadratic Dirichlet L-functions over the rational function field 𝔽_q(t), where q is a power of 2.

• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.473-482
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• 2010

In the present paper we define a q-extension of the Leibniz rule for q-derivatives via Weyl type q-derivative operator. Expansions and summation formulae for the generalized basic hypergeometric functions of one and more variables are deduced as the applications of the main result.

• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.505-519
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• 2018

In this paper we define a (p, q)-Laplace transform. By using this definition, we obtain many properties including the linearity, scaling, translation, transform of derivatives, derivative of transforms, transform of integrals and so on. Finally, we solve the differential equation using the (p, q)-Laplace transform.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.207-236
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• 2018

We obtain recursion formulas for q-hypergeometric and q-Appell series. We also find recursion formulas for the general double q-hypergeometric series. It is shown that these recursion relations can be expressed in terms of q-derivatives of the respective q-hypergeometric series.

• Honam Mathematical Journal
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• v.44 no.1
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• pp.26-35
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• 2022

In this paper we introduce two type of representations of the Pascal matrix via induced transformations of some q-derivatives as well as their some combinatorial applications.